Effect of viscous dissipation on mixed convection flow in a vertical double passage channel using Robin boundary conditions

Abstract

The laminar fully developed flow in a vertical double passage channel filled with clear fluid has been discussed using Robin boundary conditions. The thin perfectly conductive baffle is inserted in the channel. The governing equations of the fluid which are coupled and nonlinear are solved analytically by the perturbation method and semi analytically using differential transform method (DTM). The reference temperature of the external fluid is considered to be equal and different. The perturbation method which is valid for small values of perturbation parameter is used to find the combined effects of buoyancy forces and viscous dissipation. The limitation imposed on the perturbation parameter is relaxed by solving the basic equations using differential transform method. The influence of mixed convection parameter, Biot number for symmetric and asymmetric wall temperatures on the velocity, temperature and the Nusselt number is explored at different positions of the baffle. The solutions obtained by differential transform method are justified by comparing with the solutions obtained by perturbation method and the solutions agree very well for small values of the perturbation parameter.

Keywords: Baffle, Differential Transform Method, Perturbation Method, Viscous dissipation, Robin Boundary Conditions, Double passage channel.